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Han-era mathematical achievements include solving problems with right-angle triangles, square roots, cube roots, and matrix methods, finding more accurate approximations for pi, providing mathematical proof of the Pythagorean theorem, use of the decimal fraction, Gaussian elimination to solve linear equations, and continued fractions to find the roots of equations.
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Han-era and methods
In southern and small parts of central Han-era China, paddy fields were chiefly used to grow rice, while farmers along the Huai River used transplantation methods of rice production.
Han-era and for
Architectural historian Robert L. Thorp points out the scarcity of Han-era archaeological remains, and claims that often unreliable Han-era literary and artistic sources are used by historians for clues about lost Han architecture.
Some Russian archaeologists have identified a Han-era Chinese-style palace unearthed near Abakan ( in Southern Siberia ) in 1941-45 as Lu Fang's residence after he had left China for the lands of the Xiongnu.
Han-era and use
Han-era Daoists assembled into small groups of hermits who attempted to achieve immortality through breathing exercises, sexual techniques and use of medical elixirs.
Han-era and .
The Han-era family was patrilineal and typically had four to five nuclear family members living in one household.
The bloomery was nonexistent in ancient China ; however, the Han-era Chinese produced wrought iron by injecting excess oxygen into a furnace and causing decarburization.
The Han-era Chinese used bronze and iron to make a range of weapons, culinary tools, carpenters ' tools and domestic wares.
Over ten Han-era underground tombs have been found, many of them featuring archways, vaulted chambers, and domed roofs.
Evidence of Han-era mechanical engineering comes largely from the choice observational writings of sometimes disinterested Confucian scholars.
Han-era astronomers adopted a geocentric model of the universe, theorizing that it was shaped like a sphere surrounding the earth in the center.
The Han-era Chinese sailed in a variety of ships differing from those of previous eras, such as the tower ship.
Han-era medical physicians believed that the human body was subject to the same forces of nature that governed the greater universe, namely the cosmological cycles of yin and yang and the five phases.
Thus, Han-era physicians prescribed medicine that was believed to counteract this imbalance.
They rule Han-era China from behind a puppet emperor and wish to spread their power throughout the timestream.
mathematical and achievements
As his main mathematical achievements (" maître-thèmes "), he chose this collection of 12 topics ( his chronological order ):
One of the most vigorous and fruitful branches of mathematics [...] a paradise created by Cantor from which nobody shall ever expel us [...] the most admirable blossom of the mathematical mind and altogether one of the outstanding achievements of man's purely intellectual activity.
; Nikolai Nikolaevich Krasovsky: for outstanding achievements in the mathematical theory of control and the theory of differential games.
The development of mathematical proof is primarily the product of ancient Greek mathematics, and one of its greatest achievements.
Godfrey Harold " G. H ." Hardy FRS ( 7 February 1877 – 1 December 1947 ) was an English mathematician, known for his achievements in number theory and mathematical analysis.
His mathematical achievements included:
There is a study of his philosophy in Francisque Bouillier, Histoire de la philosophie cartésienne ( Paris, 1868 ); and his mathematical achievements are discussed by Franz Bopp in the 14th volume of the Abhandlung zur Geschichte der mathematischen Wissenschaften ( Leipzig, 1902 ).
* MacTutor biography, focusing on mathematical achievements
Their ideas used recent achievements in biological fisheries modelling, primarily the works by Schaefer ( 1957 ) on establishing a formal relationship between fishing activities and biological growth through mathematical modelling confirmed by empirical studies, and also relates itself to ecology and the environment and resource protection.
Apart from his outstanding organizational talent, Courant is well remembered for his mathematical achievements.
The " Mathematica: A World of Numbers ... and Beyond " exhibit detailed the major achievements in the history of mathematics from the twelfth century as well as explaining mathematical formulae including Kepler's laws of planetary motion and probability theory.
It was given for " outstanding creative work in the fields of science and technology, important mathematical and scientific discoveries and technological inventions, the introduction of new working and production methods " and " outstanding works and achievements in the areas of art and literature.
mathematical and include
Statements in this class include the statement that P = NP, the Riemann hypothesis, and many other unsolved mathematical problems.
Manufacture include bells, mathematical instruments, electrical goods, cotton textiles, chemicals, shoes, and other products.
Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a lake.
Commonly used types of data include life history, fecundity, and survivorship, and these are analysed using mathematical techniques such as matrix algebra.
Such concerns include mathematical well-posedness: the existence, uniqueness, and stability of any solutions to econometric equations.
Examples of ideograms include wayfinding signs, such as in airports and other environments where many people may not be familiar with the language of the place they are in, as well as Arabic numerals and formal languages ( mathematical notation, logic, UML ), which are used worldwide regardless of how they are pronounced in different languages.
Areas where differences have been found include verbal and mathematical ability.
When it is considered that some e-learning courses need to include video, mathematical equations using MathML, chemistry equations using CML and other complex structures the issues become very complex, especially if the systems needs to understand and validate each structure and then place it correctly in a database.
The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.
Other mathematical principles evidenced in his works include the superposition of a hyperbolic plane on a fixed 2-dimensional plane, and the incorporation of three-dimensional objects such as spheres, columns and cubes into his works.
In general, mathematical models may include logical models, as far as logic is taken as a part of mathematics.
Plato's Forms include numbers and geometrical figures, making them a theory of mathematical realism ; they also include the Form of the Good, making them in addition a theory of ethical realism.
Other mathematical developments in radar signal processing include time-frequency analysis ( Weyl Heisenberg or wavelet ), as well as the chirplet transform which makes use of the change of frequency of returns from moving targets (" chirp ").
Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry, a mathematical relation between bosons and fermions.
The mathematical techniques used include denotational semantics, axiomatic semantics, operational semantics, and abstract interpretation.
Some of the notable mathematical concepts named after Banach include Banach spaces, Banach algebras, the Banach – Tarski paradox, the Hahn – Banach theorem, the Banach – Steinhaus theorem, the Banach-Mazur game, the Banach – Alaoglu theorem and the Banach fixed-point theorem.
Further examples include some of the early versions of the pixel shader languages embedded in Direct3D and OpenGL extensions, or a series of mathematical formulae in a spreadsheet with no cycles.
Other " miscellaneous " research areas in theoretical chemistry include the mathematical characterization of bulk chemistry in various phases ( e. g. the study of chemical kinetics ) and the study of the applicability of more recent math developments to the basic areas of study ( e. g. for instance the possible application of principles of topology to the study of elaborate electronic structure ).
Possible mathematical definitions for the spoiler effect include failure of the independence of irrelevant alternatives ( IIA ) axiom, and vote splitting.
Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
Hilary Putnam has argued that any theory of mathematical realism would include quasi-empirical methods.
In mathematics, several specific infinite sequences of bits have been studied for their mathematical properties ; these include the Baum – Sweet sequence, Ehrenfeucht – Mycielski sequence, Fibonacci word, Kolakoski sequence, regular paperfolding sequence, Rudin – Shapiro sequence, and Thue – Morse sequence.
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